Asked by Albert Finger noodle
Which line is parallel to the line y=−2x−4
and goes through the point (2, 1)
?(1 point)
Responses
y=−2x+5
y is equal to negative 2 x plus 5
y=−1/2x+5
y is equal to negative 1 half x plus 5
y=−2x−4
y is equal to negative 2 x minus 4
y=1/2x
y is equal to 1 half x
and goes through the point (2, 1)
?(1 point)
Responses
y=−2x+5
y is equal to negative 2 x plus 5
y=−1/2x+5
y is equal to negative 1 half x plus 5
y=−2x−4
y is equal to negative 2 x minus 4
y=1/2x
y is equal to 1 half x
Answers
GPT-4o mini
To find a line that is parallel to the line \( y = -2x - 4 \) and goes through the point \( (2, 1) \), we first note that parallel lines have the same slope. The slope of the given line is \(-2\).
Next, we use the point-slope form of the equation of a line, which is
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Here, \( m = -2 \) and the point is \( (2, 1) \). Substituting these values gives us:
\[
y - 1 = -2(x - 2)
\]
Now, simplify this equation:
\[
y - 1 = -2x + 4
\]
\[
y = -2x + 5
\]
Thus, the equation of the line that is parallel to \( y = -2x - 4 \) and passes through the point \( (2, 1) \) is:
\[
y = -2x + 5
\]
So the correct response is:
**y=−2x+5**
Next, we use the point-slope form of the equation of a line, which is
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Here, \( m = -2 \) and the point is \( (2, 1) \). Substituting these values gives us:
\[
y - 1 = -2(x - 2)
\]
Now, simplify this equation:
\[
y - 1 = -2x + 4
\]
\[
y = -2x + 5
\]
Thus, the equation of the line that is parallel to \( y = -2x - 4 \) and passes through the point \( (2, 1) \) is:
\[
y = -2x + 5
\]
So the correct response is:
**y=−2x+5**